Learn how to calculate probability and payouts in slots

In today's little math exercise, we'll show you how to count probability in slot machines.

First of all, we must start with the number of possible combinations. In the case of slots, it is relatively simple – just multiply the numbers of symbols on each reel. The oldest slots had, for example, 3 reels with ten different symbols on each. The total number of combinations that could appear on the panel was 1,000 (10 x 10 x 10).

The number of combinations in today’s slots is somewhat higher. If we assume five reels with 30 symbols on each, we get a total of 243,000,000 combinations.

If you want to calculate your chances to win on an online slot machine, all you need is this simple equation:

Number of winning combinations / Total number of combinations

To calculate the payout of the slot machine, modify the formula a little:

Let’s analyze a few basic slot machines. For the purposes of our article and in order to simplify the calculation, we will assume that the slot machine has only one payout line and the bet is one coin per round.

Analysis of the simplest slot machine

Let’s go back to the past and assume that the machine only has 3 reels and there is an apple, an orange, a lemon, a banana, a melon and a joker symbol on each. The individual combinations produce these winnings:

Three jokers win 30 coins

Any three fruits win 10 coins

Two jokers win 4 coins

One joker wins 1 coin

The total number of combinations is 216 (6 x 6 x 6).

Total number of winning combinations:

In the first case there is only one winning combination (1 x 1 x 1 = 1)

In the second case we have 5 winning combinations (3 times apple or 3 times orange or 3 times lemon, …) (1 x 1 x 1) x 5 = 5

Calculation of payouts according to the formula

In this case, the slot machine has a payout ratio of 99.53%, which is very nice, but in a real casino, you will not find the same results. The average returns of slots online casinos will be between 94% and 98%.

The table also clearly shows how single coin wins affect payouts. If the win of each combination were equal to one coin, the winning ratio would drop to 44.4%. And that’s a very small number.

Analysis of a more complicated slot

Because the previous example was too distant from reality, let’s show you another example with higher numbers. To simplify, let’s assume again that there is only one payline, the slot machine has 3 reels and a total of 6 symbols that can appear on the panel:

The following table shows the amount of payout and the chance of winning for the individual combinations.

Winning combination

Number of combinations

Winning

Returns for 1 coin

Chance to win

3x BAR

1

60

60

0.495%

3x SEVEN

3

40

120

0.989%

3x Cherry

36

20

720

5.934%

3x Other fruit

540

10

5,400

44.507%

2x Cherry

651

3

1,935

16.097%

1x Cherry

3,880

1

3,880

31.979%

Total

5,111

12,133

% of winning combinations

42.007%

Payout

99.721%

As you can see, the payout ratio is very high again at 99.721% (12,133 / 12,161). If the slot were to pay a straight win for each winning combination in the amount of 1 coin, the payout ratio would be down to 42,007%.